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Multiscale Variance Reduction Methods Based on Multiple Control Variates for Kinetic Equations with Uncertainties
Multiscale Modeling and Simulation ( IF 1.9 ) Pub Date : 2020-02-25 , DOI: 10.1137/18m1231985
Giacomo Dimarco , Lorenzo Pareschi

Multiscale Modeling &Simulation, Volume 18, Issue 1, Page 351-382, January 2020.
The development of efficient numerical methods for kinetic equations with stochastic parameters is a challenge due to the high dimensionality of the problem. Recently we introduced a multiscale control variate strategy which is capable of considerably accelerating the slow convergence of standard Monte Carlo methods for uncertainty quantification. Here we generalize this class of methods to the case of multiple control variates. We show that the additional degrees of freedom can be used to further improve the variance reduction properties of multiscale control variate methods.


中文翻译:

不确定动力学方程的基于多控制变量的多尺度方差降低方法

《多尺度建模与仿真》,第18卷,第1期,第351-382页,2020年1月
。由于问题的高维性,开发具有随机参数的动力学方程的有效数值方法是一项挑战。最近,我们引入了一种多尺度控制变量策略,该策略能够大大加快标准蒙特卡罗方法用于不确定性量化的缓慢收敛。在这里,我们将这类方法推广到多个控制变量的情况。我们表明,附加的自由度可用于进一步改善多尺度控制变量方法的方差减少性质。
更新日期:2020-02-25
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